超声弯曲模式变幅杆的研究
文献类型：学位论文
| 作者 | 周光平 |
| 学位类别 | 博士 |
| 答辩日期 | 1999 |
| 授予单位 | 中国科学院声学研究所 |
| 授予地点 | 中国科学院声学研究所 |
| 关键词 | 超声弯曲模式 变幅杆 |
| 中文摘要 | 超声振动系统是大功率超声设备的核心部件，其中变幅杆的作用是进行位移振幅的放大。在常用超声频和振动系统的尺寸范围内，Timoshenko理论能很好地满足精度要求。本文基于Timoshenko理论，利用传递矩阵法，对由不同材料和不同截面在小的等截面杆组成的复合杆进行了振动分析。进一步，本文把变幅杆，即一般变截面杆，看成由若干等截面单元杆组成，这样把复合杆的分析方法直接应用到变幅杆上，得到了弯曲变幅杆分析的近似解析法。推导了变幅杆谐振方程、放大系数与形状因子的表达式，同时给出了变幅杆位移、应力分面的计算方法。为对这种近似解析法进行验证，试制了几个变幅杆，对其共振频率进行了测量；由于微小振幅测量上的困难，对放大系数用商用有限元程序进行了计算；实验与有限元计算与本文所用近似解析法计算结果吻合很好。利用数值计算法，对常用单一和复合变幅杆的特性进行了系统研究并介绍了弯曲变幅杆对弯曲振动系统的设计方法。对单一变幅杆的谐振特性研究表明：对一定长度的变幅杆，随着变幅杆直径的增大，指数形、锥形、悬链线形变幅杆的谐振频率是升高的；对一定端直径的变幅杆，随着变幅杆长度的增加，其谐辰频率都是下降的。研究指出，变幅杆谐辰频率与其尺寸参量间满足一定关系，本文用“谐振曲线”来描述这种关系，并给出了指数形、锥形和悬链线形杆的谐振曲线。谐振曲线可用来进行工程设计，另外，它为变幅杆复合振动的研究提供了有力的工具。对几种常用单一变幅杆的放大系数和形态因子的研究表明：同样尺寸的变幅杆，在高阶模式时放大系数变大，形状因子变小；端直径相同，工作在同模式频率，不同类变幅杆放大系数按从大到小的顺序排列是悬链线形>指数形>锥形；形状因子大小排列顺序正好相反。对阶梯杆，在二阶模式以下，规律与上同，其放大系数是最大的，形状因子是最小的。与纵向振动系统不同，弯曲振动系统不满足“半波长”迭加规律，因此，本文介绍了设计方法。一般变幅杆的分析和设计都是在空载条件下进行的，而实际应用中是有负载的。为了解负载的影响，利用输入阴抗法，提出了变曲变幅杆负载特性分析法，给出了有负载时，变幅杆共振频率及放大系数的表达式，以及位移、应力分布的求法。作为方法的应用例子，以典型的集中质量负载和力阻负载，研究了它对变幅杆共振频率和放大系数的影响。介绍了Mobius变换分析在阻抗分析中的应用。传统超声振动系统多采用单一振动模式，复合振动扩大了其应用范围。本文对指数形，锥形和悬链线形杆的纵-变、扭-弯和纵-扭复合振动进行了研究。以纵-弯复合振动为例，对一维结构超声振动系统的复合振动进行了研究。 |
| 英文摘要 | The ultrasonic vibration system is the key part of any power ultrasonic equipment, in which the solid horns act as amplifiers, which magnify vibration displacement. in the realm of common use ultrasonic frequencies and sizes of vibration system, Timoshenko theory is applicable. Based on Timoshenko theory and by using the transfer matrix method, this paper analyzed composite beam composing of uniform beams with different material or cross-section areas. Further, by dividing a solid horn, i.e. a nonuniform beam into a number of uniform element beams, an approximate analytic method is presented for analyzing flexural solid horn. The equations are derived for resonant frequency, magnification and shape factor of a flexural solid horn. The method is given for calculating the displacement and stress distribution of a horn. To verify the approximate analytic method, several solid horns are manufactured and their flexural resonant frequencies are measured. Limited by the experimental condition the magnification was not verified experimentally. As a comparison, the magnification was computed by finite element method (FEM). The results of the method agree well with the results of experiment and FEM. By using numerical calculation method, the vibration characteristics are investigated systematically of simple and composite solid horns. In addition, the design method of flexural-solid horn and vibration system is given. The study on resonant characteristics of simple horns shows that for certain length of horn the resonant frequency of exponential, conic, and catenary horns increases when the large end diameter or the small end diameter increases and that for certain end diameters the frequency decreases when the length increases. In addition, the relation between resonant frequency and size parameters of the three types of horns conform to the resonant curves. A part of resonant curves are given for the three types of horns. The curves can be used for design of horns and for the study of complex vibration of horns. The study on magnification and shape factor of simple horns shows that: for a solid horn with certain sizes. The magnification is greater and the shape factor is smaller when operating at higher mode; for given end diameters, and operating at the same frequency of the same made, the magnification of the catenary horn is greater than that of the exponential horn, which is in succession greater than that of the conic horn; for shape factor it is just the opposition; for step horn, the above rules are valid when operating under the second model. A design method is presented in the consideration that the conception of half-wavelength cascade is not applicable as in the design of longitudinal vibration system. In practical application there exist loads on solid horn. A method is presented for analyzing the load characteristics of horn by using input impedance method. The equations of resonant frequency and magnification are derived for loaded horn. The method for calculating displacement and stress distribution is also given for loaded horn. Taking typical mass and resistance load as example, the influence of load on resonant frequency nd magnification of horn are studied. Finally, Mobius transformation is introduced to the impedance analysis of horn. The realization of complex-mode vibration system expanded power ultrasonic application. The complex vibration is investigated of exponential, conic and catenary horns operating longitudinal-flexural, torsional-flexural and longitudinal-torsional complex vibration. Taking longitudinal-flexural complex vibration as an example, the complex vibration of vibration system with one dimensional construction is studied. |
| 语种 | 中文 |
| 公开日期 | 2011-05-07 |
| 页码 | 118 |
| 源URL | [http://159.226.59.140/handle/311008/610]  |
| 专题 | 声学研究所_声学所博硕士学位论文_1981-2009博硕士学位论文 |
| 推荐引用方式 GB/T 7714 | 周光平. 超声弯曲模式变幅杆的研究[D]. 中国科学院声学研究所. 中国科学院声学研究所. 1999. |
入库方式： OAI收割
来源：声学研究所
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